I'm so sorry to hear of the loss of your grandma, please be kind to yourself 
The only thing I can offer by way of advice is to try and remember that grief does strange things to us all and rarely are people at their best or most rational in the wake of a death. The loss of someone you've cared for for a long time can be particularly tricky emotionally because there are often feelings of relief and release alongside the 'pure' sadness of the loss, plus horrible memories of the person when they were unwell sometimes intrude alongside the happy ones (I don't know how your grandma's dementia took her but one of my relatives turned very angry and spiteful towards the end and it was hard at first to not remember that version of him, and the versions of ourselves it turned us into, rather than the person/people we knew and loved, thankfully this eased a lot over time), and there can be a lot of shame, anxiety (did I do my best for the person? If I'd done XYZ would it have been better? etc) and guilt (I shouted at her that day, this day I didn't come to her when she called etc) wrapped up in this which can turn people irritable or defensive. Plus, and this is hard to explain, you also get this feeling of additional loss, the fact of the years 'lost' to the illness can suddenly hit you plus the realization you will never get the 'well' person back again - even though rationally you knew the illness was incurable, while the person was alive you always have hope you might get at least a glimpse of the 'real them' from time to time or perhaps even that a miracle would happen, whereas when they're gone, that's it. And also it can be a reminder of your own impending mortality if you suddenly find yourself going from the active, carer role to the 'elder' generation of your family with the loss of the last of the older one?
I've probably not explained that well, sorry but I guess what I'm saying is that grief can sometimes feel really confusing and shameful and lonely and as though you are beyond comfort, and so even the most loving and well meaning of relatives offering perfectly good and caring help and support can tend up getting lashed out at for no good reason. I'm sure your Mum really doesn't mean to reject your help and please don't feel like a bad daughter or granddaughter for offering it .
I would keep doing what you are doing, keep the communications open even if you feel you're just getting trivial or snappy responses back, keep offering help with the practicalities but let your mum do it all if this is a comfort to her (we have a few people in our family who insist on being the ones to do absolutely everything in the wake of a death, even to the point of absolutely exhausting themselves, it's a bit annoying and totally unnecessary but it seems to be their way of coping). Try and find time to see her in person but phone calls and texts in between times are good too, you can only do what you can. You can ask her as well, mum what would be best for me to do for your (don't say 'how can I help' or 'what would make it better' because the answer might come back 'nothing!). Be really kind to yourself too, have you got someone to take care of you? Don't engage mentally in hierarchies of loss, just because the loss is "worse" for your mum doesn't mean you don't get to grieve too or you aren't allowed to cry. If long walks and talking about her or just having someone to sit quietly with would be a help can your partner (if you have one) or another relative or friend do this for you?